Blue large-amplitude pulsators (BLAPs) represent a new and rare class of hot pulsating stars with unusually large amplitudes and short periods. The evolutionary path that could give rise to such kinds of stellar configurations is unclear. Here we report a comprehensive study ofthe peculiar BLAP discovered by the Tsinghua University-Ma Huateng Telescopes for Survey (TMTS), namely, TMTSJ035143.63+584,504.2 (TMTS-BLAP-1). This new BLAP has an 18.9 min pulsation period and is similar to the BLAPs with a low surface gravity and extended helium-enriched envelope, suggesting that it is a low-gravity BLAP at the shortest-period end. In particular, the long-term monitoring data reveal that this pulsating star has an unusually large rate of period change, namely, (P) over dot/P = 2.2 x 10(-6) yr(-1). Such a significant and positive value challenges its origins from both helium-core pre-white-dwarfs and core helium-burning subdwarfs, but is consistent with that derived from shell helium-burning subdwarfs. The particular pulsation period and unusual rate of period change indicate that TMTS-BLAP-1 is at a short-lived (similar to 10(6) yr) phase of shell helium ignition before the stable shell helium burning; in other words, TMTS-BLAP-1 is going through a 'Hertzsprung gap' of hot subdwarfs.